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Querying and Mining of Time Series Data: Experimental Comparison of Representations and Distance Measures
"... The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introduci ..."
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Cited by 141 (24 self)
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The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive set of time series experiments reimplementing 8 different representation methods and 9 similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this paper, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. Our experiments have provided both a unified validation of some of the existing achievements, and in some cases, suggested that certain claims in the literature may be unduly optimistic. 1.
Searching Trajectories by Locations – An Efficiency Study
"... Trajectory search has long been an attractive and challenging topic which blooms various interesting applications in spatialtemporal databases. In this work, we study a new problem of searching trajectories by locations, in which context the query is only a small set of locations with or without an ..."
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Cited by 29 (11 self)
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Trajectory search has long been an attractive and challenging topic which blooms various interesting applications in spatialtemporal databases. In this work, we study a new problem of searching trajectories by locations, in which context the query is only a small set of locations with or without an order specified, while the target is to find the k BestConnected Trajectories (kBCT) from a database such that the kBCT best connect the designated locations geographically. Different from the conventional trajectory search that looks for similar trajectories w.r.t. shape or other criteria by using a sample query trajectory, we focus on the goodness of connection provided by a trajectory to the specified query locations. This new query can benefit users in many novel applications such as trip planning. In our work, we firstly define a new similarity function for measuring how well a trajectory connects the query locations, with both spatial distance and order constraint being considered. Upon the observation that the number of query locations is normally small (e.g. 10 or less) since it is impractical for a user to input too many locations, we analyze the feasibility of using a generalpurpose spatial index to achieve efficient kBCT search, based on a simple Incremental kNN based Algorithm (IKNN). The IKNN effectively prunes and refines trajectories by using the devised lower bound and upper bound of similarity. Our contributions mainly lie in adapting the bestfirst and depthfirst kNN algorithms to the basic IKNN properly, and more importantly ensuring the efficiency in both search effort and memory usage. An indepth study on the adaption and its efficiency is provided. Further optimization is also presented to accelerate the IKNN algorithm. Finally, we verify the efficiency of the algorithm by extensive experiments.
Efficient knearest neighbor search on moving object trajectories
, 2009
"... With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatiotemporal databases. In this paper we consider the following problem: Given a se ..."
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Cited by 20 (3 self)
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With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatiotemporal databases. In this paper we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the life time of mq. We assume D is indexed in a 3DRtree and employ a filterandrefine strategy. The filter step traverses the index and creates a stream of socalled units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result. To support the filter step, for each node p of the index, in preprocessing a time dependent coverage function Cp(t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the Rtree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient kNN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin. Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.
Experimental comparison of representation methods and distance measures for time series data
 Data Mining and Knowledge Discovery
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Finding Long and Similar Parts of Trajectories
, 2011
"... A natural timedependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly selfintersecting lines with tim ..."
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Cited by 11 (4 self)
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A natural timedependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly selfintersecting lines with time stamps. For the case when a minimum duration of the subtrajectories is specified and the subtrajectories must start at corresponding times, we give a lineartime algorithm. The algorithm is based on a result of independent interest: We present a lineartime algorithm to find, for a piecewise monotone function, an interval of at least a given length that has minimum average value. In the case that the subtrajectories may start at noncorresponding times, it appears difficult to give exact algorithms, even if the duration of the subtrajectories is fixed. For this case, we give (1 + ε)approximation algorithms, for both fixed duration and when only a minimum duration is specified. 1
On Efficiently Searching Trajectories and Archival Data for Historical Similarities
, 2008
"... We study the problem of efficiently evaluating similarity queries on histories, where a history is a ddimensional time series for d ≥ 1. While there are some solutions for timeseries and spatiotemporal trajectories where typically d ≤ 3, we are not aware of any work that examines the problem for l ..."
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Cited by 6 (0 self)
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We study the problem of efficiently evaluating similarity queries on histories, where a history is a ddimensional time series for d ≥ 1. While there are some solutions for timeseries and spatiotemporal trajectories where typically d ≤ 3, we are not aware of any work that examines the problem for larger values of d. In this paper, we address the problem in its general case and propose a class of summaries for histories with a few interesting properties. First, for commonly used distance functions such as the Lpnorm, LCSS, and DTW, the summaries can be used to efficiently prune some of the histories that cannot be in the answer set of the queries. Second, histories can be indexed based on their summaries, hence the qualifying candidates can be efficiently retrieved. To further reduce the number of unnecessary distance computations for false positives, we propose a finer level approximation of histories, and an algorithm to find an approximation with the least maximum distance estimation error. Experimental results confirm that the combination of our feature extraction approaches and the indexability of our summaries can improve upon existing methods and scales up for larger values of d and database sizes, based on our experiments on real and synthetic datasets of 17dimensional histories.
Efficient Similarity Join of Large Sets of Moving Object Trajectories
"... We address the problem of performing efficient similarity join for large sets of moving objects trajectories. Unlike previous approaches which use a dedicated index in a transformed space, our premise is that in many applications of locationbased services, the trajectories are already indexed in th ..."
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Cited by 5 (1 self)
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We address the problem of performing efficient similarity join for large sets of moving objects trajectories. Unlike previous approaches which use a dedicated index in a transformed space, our premise is that in many applications of locationbased services, the trajectories are already indexed in their native space, in order to facilitate the processing of common spatiotemporal queries, e.g., range, nearest neighbor etc. We introduce a novel distance measure adapted from the classic Fréchet distance, which can be naturally extended to support lower/upper bounding using the underlying indices of moving object databases in the native space. This, in turn, enables efficient implementation of various trajectory similarity joins. We report on extensive experiments demonstrating that our methodology provides performance speedup of trajectory similarity join by more than 50 % on average, while maintaining effectiveness comparable to the wellknown approaches for identifying trajectory similarity based on timeseries analysis. 1
User oriented trajectory search for trip recommendation
 In Proc. ACM EDBT
, 2012
"... ABSTRACT Trajectory sharing and searching have received significant attentions in recent years. In this paper, we propose and investigate a novel problem called User Oriented Trajectory Search (UOTS) for trip recommendation. In contrast to conventional trajectory search by locations (spatial domain ..."
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Cited by 4 (0 self)
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ABSTRACT Trajectory sharing and searching have received significant attentions in recent years. In this paper, we propose and investigate a novel problem called User Oriented Trajectory Search (UOTS) for trip recommendation. In contrast to conventional trajectory search by locations (spatial domain only), we consider both spatial and textual domains in the new UOTS query. Given a trajectory data set, the query input contains a set of intended places given by the traveler and a set of textual attributes describing the traveler's preference. If a trajectory is connecting/close to the specified query locations, and the textual attributes of the trajectory are similar to the traveler'e preference, it will be recommended to the traveler for reference. This type of queries can bring significant benefits to travelers in many popular applications such as trip planning and recommendation. There are two challenges in the UOTS problem, (i) how to constrain the searching range in two domains and (ii) how to schedule multiple query sources effectively. To overcome the challenges and answer the UOTS query efficiently, a novel collaborative searching approach is developed. Conceptually, the UOTS query processing is conducted in the spatial and textual domains alternately. A pair of upper and lower bounds are devised to constrain the searching range in two domains. In the meantime, a heuristic searching strategy based on priority ranking is adopted for scheduling the multiple query sources, which can further reduce the searching range and enhance the query efficiency notably. Furthermore, the devised collaborative searching approach can be extended to situations where the query locations are ordered. The performance of the proposed UOTS query is verified by extensive experiments based on real and synthetic trajectory data in road networks.
Common Dissimilarity Measures are Inappropriate for Time Series Clustering
"... Abstract: Clustering algorithms have been actively used to identify similar time series, providing a better understanding of data. However, common clustering dissimilarity measures disregard time series correlations, yielding poor results. In this paper, we introduce a dissimilarity measure based o ..."
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Abstract: Clustering algorithms have been actively used to identify similar time series, providing a better understanding of data. However, common clustering dissimilarity measures disregard time series correlations, yielding poor results. In this paper, we introduce a dissimilarity measure based on series partial autocorrelations. Experiments compare hierarchical clustering algorithms using the common dissimilarity measures, such as Euclidean Distance and Dynamic Time Warping, to cluster time series following BoxJenkins AutoRegressive models. Results show that our dissimilarity measure produces better results for both synthetic and real data sets in terms of the Adjusted Rand Index and Normalized Hubert Γ statistic. Our findings confirm that the choice of dissimilarity measure is crucial for improving time series clustering quality. 1
Trajectory Pattern Matching Based on BitParallelism for Large GPS Data
"... AbstractIn this paper, we consider an approximate search problem for massive trajectory data. We first propose multiresolution symbolic encoding for 2dimnetional trajectory data based on a fixedlength stopper code. Then, we present an efficient bitparallel string matching algorithm on encoded t ..."
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AbstractIn this paper, we consider an approximate search problem for massive trajectory data. We first propose multiresolution symbolic encoding for 2dimnetional trajectory data based on a fixedlength stopper code. Then, we present an efficient bitparallel string matching algorithm on encoded texts for the classes of multiresolution trajectory patterns. Finally, we ran experiments on the real world trajectory data to evaluate the efficiency of the proposed algorithm. The results showed good performance enough for real applications.